Top-quark production at approximate N$^3$LO

I discuss recent theoretical results with soft-gluon corrections for various top-quark production processes through approximate N$^3$LO, including soft anomalous dimensions through three loops. I present numerical results for total cross sections and differential distributions for top-pair and $tW$ production as well as for three-particle final states with a top quark and a Higgs boson. I show that soft-gluon corrections are dominant for a large range of collider energies.